Exploring the relativistic regime with Newtonian hydrodynamics: an improved effective gravitational potential for supernova simulations

By Andreas Marek, H. Dimmelmeier, Hans-Thomas Janka, E. Mueller, R. Buras. 2005

224 citations recorded by the source corpus.

We investigate the possibility approximating relativistic effects in hydrodynamical simulations of stellar core collapse and post-bounce evolution by using a modified gravitational potential in an otherwise standard Newtonian hydrodynamic code. Different modifications of a previously introduced effective relativistic potential are discussed. Corresponding hydrostatic solutions are compared with solutions of the TOV equations, and hydrodynamic simulations with two different codes are compared with fully relativistic results. One code is applied for one- and two-dimensional calculations with a simple equation of state and employs either the modified effective relativistic potential in a Newtonian framework or solves the general relativistic field equations under the assumption of the conformal flatness condition (CFC) for the three-metric. The second code allows for full-scale supernova runs including a microphysical equation of state and neutrino transport based on the solution of the Boltzmann equation and its moments equations. We present prescriptions for the effective relativistic potential for self-gravitating fluids to he used in Newtonian codes, which produce excellent agreement with fully relativistic solutions in spherical symmetry, leading to significant improvements compared to previously published approximations. Moreover, they also approximate qualitatively well relativistic solutions for models with rotation.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/b5dcd6eb66ac56c3e777e80dfb88c1cdb2e75ae3

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Citations in the corpus

Equation-of-state dependent features in shock-oscillation modulated neutrino and gravitational-wave signals from supernovae (2008, methodology): “…equations of motions for the stellar fluid, whose self-gravity is described by an “effective relativistic potential” for an approximative treatment of general relativistic gravity (see Marek et al. 2006, the discussed simulations were performed with the potential of Case A from this work).”
NEUTRINO-DRIVEN EXPLOSION OF A 20 SOLAR-MASS STAR IN THREE DIMENSIONS ENABLED BY STRANGE-QUARK CONTRIBUTIONS TO NEUTRINO–NUCLEON SCATTERING (2015, methodology): “We used a 1D gravity potential (which is unproblematic for strongly PNS-dominated gravity fields) including general relativistic corrections (Marek et al. 2006).”
A NEW MULTI-DIMENSIONAL GENERAL RELATIVISTIC NEUTRINO HYDRODYNAMIC CODE FOR CORE-COLLAPSE SUPERNOVAE. I. METHOD AND CODE TESTS IN SPHERICAL SYMMETRY (2010, methodology): “Since our code is largely an adapted version of the Newtonian VERTEX-PROMETHEUS code of Rampp & Janka (2002), this also allows us to better assess the reliability of the effective potential approach for GR effects (Rampp & Janka 2002; Marek et al. 2006; now also used, e.g., by Messer et al. 2007).”
The overarching framework of core-collapse supernova explosions as revealed by 3D fornax simulations (2019, methodology): “The monopole gravitational term is altered to approximately accommodate general-relativistic gravity (Marek et al. 2006) and we employ the metric terms, grr and gtt, derived from this potential in the neutrino transport equations to incorporate general relativistic redshift effects (in the manner…”
Multidimensional supernova simulations with approximative neutrino transport. I. Neutron star kicks and the anisotropy of neutrino-driven explosions in two spatial dimensions (2006, methodology): “In our calculations, his turned out to yield very good agreement with the improved version of the effective relativistic potential developed by Marek et al. (2006).”
SASI ACTIVITY IN THREE-DIMENSIONAL NEUTRINO-HYDRODYNAMICS SIMULATIONS OF SUPERNOVA CORES (2013, background): “In the simulations presented here, we assume monopolar gravity, but include general relativistic corrections by means of an effective gravitational potential (Marek et al. 2006).”
Origin of the heaviest elements: The rapid neutron-capture process (2019, methodology): “Newtonian 3D MHD simulations with an effective GR gravitational potential (Marek et al., 2006) and improved treatment of neutrino physics were performed by Winteler et al.”
SELF-SUSTAINED ASYMMETRY OF LEPTON-NUMBER EMISSION: A NEW PHENOMENON DURING THE SUPERNOVA SHOCK-ACCRETION PHASE IN THREE DIMENSIONS (2014, methodology): “In the simulations presented here, we adopted monopolar gravity but included general relativistic corrections by means of an effective gravitational potential (Marek et al. 2006).”
Nucleosynthesis-relevant conditions in neutrino-driven supernova outflows. I. Spherically symmetric (2006, methodology): “Marek et al. (2006) compared the neutron star structure, stability properties, and oscillation behavior obtained with the effective relativistic potential and fully relativistic calculations of nonrotating and rotating collapsing stellar iron cores.”
Gravitational wave signals from 3D neutrino hydrodynamics simulations of core-collapse supernovae (2016, methodology): “…being the treatment of GR: in G27-2D, the equations of radiation hydrodynamics in the ray-by-ray-plus approximation are solved in their general relativistic formulation assuming a conformally ﬂat metric, whereas the pseudo-Newtonian approach of Marek et al. (2006) was used for model s27 in 3D.”
A NEW MULTI-DIMENSIONAL GENERAL RELATIVISTIC NEUTRINO HYDRODYNAMICS CODE FOR CORE-COLLAPSE SUPERNOVAE. II. RELATIVISTIC EXPLOSION MODELS OF CORE-COLLAPSE SUPERNOVAE (2012, methodology): “…the result of a slightly different density stratification in GR that cannot be reproduced exactly by the modified Newtonian potential and the approximate GR transport treatment (e.g. due to the identification of coordinate radius and proper radius) used for the M15 run (cp. Marek et al. 2006).”
MAGNETOROTATIONALLY DRIVEN SUPERNOVAE AS THE ORIGIN OF EARLY GALAXY r-PROCESS ELEMENTS? (2012, unknown): “The gravitational potential is approximated by an effective axisymmetric mass distribution that includes general relativistic monopole corrections (Marek et al. 2006).”
A successful 3D core-collapse supernova explosion model (2018, methodology): “For this project, we used a monopole approximation for relativistic gravity following Marek et al. (2006), as described in Appendix A, and employed the SFHo equation of state (Steiner et al. 2013), which is consistent with all currently known nuclear constraints (Tews et al. 2017).”
Three-dimensional neutrino-driven supernovae: neutron star kicks, spins, and asymmetric ejection of nucleosynthesis products (2012, background): “Both simulation codes are Newtonian, but Prometheus-Vertex employs correction of the gravitational potential due to general relativistic effects (Marek et al. 2006).”
The Gravitational Wave Signal from Core-collapse Supernovae (2018, methodology): “The majority of simulations presented here use a monopole approximation for the approximate general-relativistic (GR) gravitational potential, following Case A of Marek et al. (2006).”